Elasticity/Principal stresses

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Principal Stresses in Two and Three Dimensions[edit | edit source]

The principal stresses are the components of the stress tensor when the basis is changed in such a way that the shear stress components become zero. To find the principal stresses in two dimensions, we have to find the angle at which . This angle is given by

Plugging into the transformation equations for stress we get,

Where are the shear tractions usually zero in a body?

The principal stresses in three dimensions are a bit more tedious to calculate. They are given by,


The quantities are the stress invariants.

Note: Be careful while implementing above relations in a solver, as the value of:

can be out of range of , which is (-1, 1).

Related Content[edit | edit source]

Introduction to Elasticity

External Links[edit | edit source]